Question

which of the following is a rational number? √2, -1, π, √6

Explanation:

Step1: Recall the definition of a rational number

A rational number is a number that can be expressed as $\frac{p}{q}$, where $p$ and $q$ are integers and $q
eq0$. Integers are also rational numbers since they can be written as $\frac{n}{1}$ (e.g., $-1=\frac{-1}{1}$).

Step2: Analyze each option

• For $\sqrt{2}$: $\sqrt{2}$ is an irrational number because it cannot be expressed as a fraction of two integers. Its decimal expansion is non - repeating and non - terminating ($\sqrt{2}\approx1.41421356\cdots$).
• For $-1$: $-1$ is an integer. As per the definition of rational numbers, integers are rational because $-1=\frac{-1}{1}$, where $p = - 1$ and $q = 1$ (both are integers and $q

eq0$).

• For $\pi$: $\pi$ is an irrational number. Its decimal expansion is non - repeating and non - terminating ($\pi\approx3.14159265\cdots$) and it cannot be expressed as a fraction of two integers.
• For $\sqrt{6}$: $\sqrt{6}$ is an irrational number. Its decimal expansion is non - repeating and non - terminating ($\sqrt{6}\approx2.44948974\cdots$) and it cannot be expressed as a fraction of two integers.

Answer:

-1 (the option with -1)